Finite Group Databasebeta

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C3×C5×D1043 #44530969

order31290
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1043
unambiguous semidirect productC149⋊(C3×C5×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C149 ⋊ C2
derived, HallC7×C149 ⋊ C2×C3×C5
HallC5×C7×C149 ⋊ C2×C3
HallC3×C7×C149 ⋊ C2×C5
HallC3×C5×C149 ⋊ D7
HallC5×C149 ⋊ C3×D7
HallC3×C149 ⋊ C5×D7
SylowC149 ⋊ C3×C5×D7
HallC3×C5×C7 ⋊ D149
HallC5×C7 ⋊ C3×D149
HallC3×C7 ⋊ C5×D149
SylowC7 ⋊ C3×C5×D149

Subgroups

subgroupG/H
center, hypercenterC3×C5D1043
commutator, cosocle, hypocenterC7×C149C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C149C2
LCSG ▷ C7×C149
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15645

Conjugacy classes & character table

7845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31290, 5);